Question

A metallic sphere of radius $4.2cm$ is melted and recast into the shape of a cylinder of radius $6cm$. Find the height of the cylinder.

Answer 1

Let the height of the cylinder be $h$ cm.

Then, volume of the cylinder $=$ Volume of the sphere

$\Rightarrow \pi \times r^2\times h=\frac{4}{3}\times \pi \times r^3$

$\Rightarrow \pi \times 6^2\times h=\frac{4}{3}\times \pi \times {\left(4.2\right)}^3$

$\Rightarrow h=\frac{4\times 4.2\times 4.2\times 4.2}{3\times 6\times 6}$

$\Rightarrow h=4\times 0.7\times 0.7\times 1.4cm$

$\Rightarrow h=2.74cm$